3/7/13 9:53 AM EST

Disney CEO Bob Iger defended the reputations of ABC News and ESPN at the company's annual shareholders meeting on Wednesday after one shareholder accused both networks of contributing to liberal media bias and the nation's declining trust in the media.

"Disney's media platforms, from ABC News to ESPN, deserve their share for the nation's skepticism -- whether its ABC News reporter Brian Ross rushing to [falsely accuse the Tea Party] for the deadly shooting and massacre at an Aurora, Colo., movie theater, or then-ESPN columnist Rob Parker saying that Washington Redskins quarterback Robert Griffin III was a, quote, 'cornball brother' who was not down with the black cause because his [fiance] is white and he is a Republican -- liberal bias pervades Disney's media outlets," Danhof, the director of the NCPPR's Free Enterprise Project, said.

"It's time to stop denying the bias and do something about it," Danhof continued. "Our company's leaders should show the intellectual honesty to admit it exists, it is a problem, and let's start working together on a solution."

Danhof argued that the appearance of such bias harmed Disney's revenue potential, because it alienated "such a large market" of conservative viewers and therefore turned away potential advertisers. Danhof cited a Feb. 2013 Gallup poll, which shows that self-identified conservatives outnumber liberals by almost two-to-one. (For the record: 38 percent of Americans identified themselves as "conservative", 36 percent as "moderate" and 23 percent as "liberal.")

"I'm not asking that you turn ABC News into Fox News, or that you start airing Glenn Beck and Rush Limbaugh daily on ESPN," Danhof said. "I'm just asking you to start playing it straight with the American people. Stop the bias and return to an era of honesty and objectivity in the news."

Iger told Danhof he respected his concerns and his right to share those concerns, but stood by both ABC News and ESPN programming.

"Our goal at ABC News and ABC News stations and at ESPN is to be fair and to present the news that they cover in as unbiased a way as possible. Without meaning to sound overly defensive, I believe that the body of their work in fact is fair and unbiased and [in]accurate," Iger said.

"However, I will say that over time we have been guilty of making mistakes -- not specifically commenting on those you cited -- but I can tell you that in managing this business over the years, we have at times either presented the news in a slightly inaccurate way through mistakes, or in ways we weren't necessarily proud of," he added. "But I firmly stand behind the integrity of our news organizations, because I believe that overall the job that they do is one that is worthy of respect, and certainly one that delivers to the value of the Walt Disney Company and its shareholders."